P A T T E R N S1.)Sierpinski's Triangle or the Sierpinski gasket

figure 3 figure 4

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figure 2

figure 1

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1.) How many green triangles are in the fourth figure?2.) How many black triangles are in the fourth figure?

(A.) Figure Green Triangles (B.) Figure Black Triangles Is there a pattern???1 12 2 3.) How many black triangles are in the 3rd figure? 4 CORRECT!3 34 45 56 67 7

4.) If the pattern continued, how many green triangles are in the nth figure? 2 SUPER!

( 1 ) 2^(n-1)( 2 ) 3^(n-1)

History: ( 3 ) 3 x (n-1)⅓ *above answer with numericals 1-4

( 4 ) 4 x (n-2)

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The Sierpinski triangle, also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self similar sets. Self similar sets are mathematically generated patterns that can be reproducible at any magnification or reduction. It is named after the Polish mathematician Waclaw Sierpinski but appeared as a decorative pattern many centuries prior to the work of Sierpinski. For more information visit: http://en.wikipedia.org/wiki/Sierpinski_triangle

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0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8

(A.) Green Triangles

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8

(B.) Black Triangles

2.) Tr iangul a r Number sNumber Dots

1234567

1 2 3 4 5

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Complete the table :

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7 8

Triangular Numbers

Math for Teachers

• http://en.wikipedia.org/wiki/Sierpinski_triangle#mediaviewer/File:Animated_construction_of_Sierpinski_Triangle.gif

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8 9 7 14 POINTS+ 2 - 4 + 8 - 6

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